Solving linear systems
Two unknowns need two equations: eliminate one variable by adding or substituting, then back-substitute for the other.
A worked example
For 4x + y = 26 and x - y = 9, adding removes y: 5x = 35, so x = 7 and then y = -2.
The mistake people actually make
Adding only cancels a variable when its coefficients are opposites; otherwise multiply an equation first. Having found one value, put it back in rather than stopping there.